Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
The paradox of the twins (devised by Einstein in person) is due to the fact that... everything is relative. If a twin leaves the Earth, travels to another planet with a speed close to the speed of light, and comes back to the Earth, this twin will be younger than the one that stayed on Earth. The reason is that clocks slow down as speed increases (time dilation).
However, according to Relativity, one can also run the experiment the other way around: from the point of view of the twin that departs the Earth, it is the Earth that travels away and then comes back. In this case, the twin who travels at high speed, and therefore who is younger, is the twin who stayed on the Earth. Thus the second twin is younger if measured from the first twin, but the first twin is younger if measured from the second twin: these measurements cannot both be true at the same time. Depending on which reference frame you use, you get two contradictory results.
Einstein solved the paradox by pointing out that the two situations are not symmetric. The twin who leaves the Earth has to apply an acceleration to get out of the Earth; then decelerate, turn and accelerate again to return to the Earth. All of this violates the principle of Relativity: the twin that departed the Earth has done something absolute.
Even if one assumes that the twin does not accelerate and decelerate, the fact remains that it changes direction. In a sense, there are three (not just two) inertial frames: the twin that stays on Earth, the twin that travels away from the Earth, and the twin that travels towards the Earth. Thus the elapsed time for the first twin is calculated by adding up two motions referred to the same frame (the Earth), whereas the elapsed time for the second twin must be calculated by adding up two motions referred to two different frames (the one moving away from the Earth and the one moving towards the Earth). Thus there is an absolute difference between the first twin measuring the second twin and the second twin measuring the first twin. The twin who becomes younger is the one leaving the Earth.
That said, it is important to remember that this "becoming younger" has nothing to do with bodily aging: it is only referred to time measured by clocks.
You can in fact dream up several "paradoxes" based on the same idea of going back and forth. Imagine, for example, that i cut a 1 cm circular hole from a sheet of paper. Now i move the sheet of paper far away, and move the circular piece high up in the air. Then i move the sheet of paper at very high speed towards the point where it will meet the circular piece that i am letting fall at a point in time such that it perfectly hits the hole. From the point of view of the circular piece, the sheet of paper is traveling at a very high speed, therefore it is shrinking, and, in particular, the hole in the middle is shrinking: therefore the circular piece will no longer be able to go through the hole. From the point of view of the sheet of paper, it is the circular piece that is traveling at very high speed, and thus shrinking: therefore the circular piece will easily pass through the hole. Imagine if instead of paper, you used spaceships: depending on which reference frame you use, the spaceships collide or they smoothly pass each other. This is not just a detail.
The solution of this second paradox is similar to the first one: we have done something at the very beginning, i.e. moving the sheet of paper far away. No matter how slowly we did that, we caused a change in its size relative to the circular hole (and viceversa). Thus, when we start moving the sheet of paper in the opposite direction, we cannot use its original size to compute the shrinking. When the sheet of paper and the circular piece meet, they are again the exact same size that they were at the beginning of the experiment.
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